Kirchhoff’s Current Law and Kirchhoff’s Voltage Law

There are two numbers of Kirchhoff’s laws. These laws are Kirchhoff’s Current Law and Kirchhoff’s Voltage Law. We use very frequently these laws in circuit analysis. The famous German Physicist Gustav Robert Kirchhoff (1824 – 1887) developed these laws.

Gustav Robert Kirchhoff
Gustav Robert Kirchhoff

Kirchhoff’s Current Law

Kirchhoff Current Law is one of the most basic laws of circuit analysis. This law works on the basis of the concept of conservation of energy.

Kirchhoff Current Law says that the sum of the currents entering at a node is exactly equal to the sum of the currents leaving the node.

This is a very basic concept. The current is the flow of charge hence it is obvious that the quantity of charge entering at a node must be leaving the node. Suppose an electrical node consists of (m + n) number of branches. Through m number of branches, currents are entering to the node. At the same time, through n numbers of branches, currents are leaving the node.

kirchhoff current law
Then we can write,

Here, we represent the currents entering the node with positive signs. On the other hand, we put a negative sign before each current leaving the node. Now, we consider that sing convention of the currents. Then we add all these signed currents. Finally, we get the result of this sum as zero. So we can say the sum of all currents at a node is zero. This is the statement of Kirchhoff’s Current Law.

Kirchhoff’s Voltage Law

Kirchhoff voltage law states that the sum of all voltage gains is equal to the sum of all voltage drops across a closed loop of a circuit. For illustrating Kirchhoff’s voltage law, we take a closed loop in an electrical circuit. Now we start from one point on the closed loop in a particular direction. After crossing all the voltages of the loop, when we come back to the same point, we will see that we come back to the same voltage level. This is because it is the same point from where we started. So we can conclude that during the journey through that closed loop, we have seen whatever voltages gain the same have been dropped. This obviously proves the statement of Kirchhoff’s Voltage Law.

Kirchhoff's Voltage Law

We take the voltage gains in a particular direction in the loop as positive. Hence, we have to take the voltage drops in that direction as negative. If we add all these voltages along with their sign we get zero as the result. We can write that as

Sign Convention of Voltages

The sign convention of voltages during applying Kirchhoff Voltage Law depends on which direction we view the loop. Generally, when we proceed from lower potential end to higher potential end of an element we consider it as voltage gain and we sign it as positive. When we proceed from the higher potential end to lower potential end of an element, we consider its voltage as a drop. Hence, we sign it as negative. For example, when a current flows through a resistance, the entry end of the current would be at a higher potential than the end through which the current leaves the resistance. Also when a current enters through the positive end of a battery and leaves from the negative end, we consider its PD as negative in respect of the direction of flow of the current.  

sign convention of voltages


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